There have been many studies at this point showing that exposure to dirt, dust, and dander early in childhood results in low rates of asthma. I'm personally fondest of the one a friend of mine (Hi Dubes!) worked on in Papua New Guinea where they found the westernization of formerly isolated cultures where dirt floors are replaced by cement results in an increase in asthma.
I recall recently hearing of a study where it was determined that when an infant's pacifier falls on the ground, and the parent cleans it by putting it in their own mouth first before returning it to the child, the children end up with substantially stronger immune systems than if the pacifier is cleaned more vigorously.
As with many aspects of developmental biology, we are born with scaffolding that needs to be trained in order to function properly. A lack of that training leads to disease. So, yes, let your kids play in the dirt.